You won't find your standard address on the blockchain. Every single output is its own one time address, there is no choice about it (as opposed to Bitcoin, where address reuse is discouraged, but commonplace, and easy to do).
Ring signatures allow transactions to be ambiguous about which outputs are spent, since any one of the N inputs in a ring signature appears to be a possible candidate.
Once RingCT is merged, transaction amounts will be fully obscured (they currently are ambiguous due to the split by denominations). Bitcoin amounts are in the clear (but may not be in the future, if CT gets merged to Bitcoin).
Auditability is based on voluntary disclosure of, depending on the task at hand, the private view key (allows a third party to see all your income, but not your spends, nor spend anything), the per tx keys (allows a third party to ascertain whether you did send a tx, as well as the amounts sent - useful for arbitration is someone claims you have not paid them), and signed key images (allows someone with your view secret key to determine which outputs of yours were spent, and which were not - essentially, your outgoings, also proof of reserves - but not where they were spent).
With Monero, nobody can see your balance from looking at the blockchain.
This is a bit of a mixed bag. Monero transactions are larger than bitcoin (typical transaction is a few kB, while in bitcoin they can easily be sub kB). Higher mixin (for better privacy) also increases transaction size.
On the other hand, Monero has no fixed blocksize limit. While there is a blocksize limit for any given block, this limit evolves based on demand in the previous blocks, allowing increasing demand to increase block size, and vice versa.
Pruning is possible both with Bitcoin and Monero. In Monero, signatures are a large part of a transaction's size (even more with RingCT), and a node does not have to keep them once they've been verified (a side effect is that this node can't serve a verifiable blockchain to other nodes after pruning). Some kind of SegWit system is also possible with Monero, though I do not know the details.
Cryptonight is heavy to verify, contrary to SHA-2. This implies CPU load on nodes, which may become significant if transaction volume increases. There has been talk of switching PoW to Cuckoo Cycle, another hash algorithm with the same goals as Cryptonight, to alleviate this.
Last, since Monero is ambiguous wrt which outputs are spent, the TXO set never decreases (or very, very seldom does), whereas with Bitcoin, spent outputs can be removed from the UTXO set.
Monero uses Cryptonight instead of SHA-2. There are currently no ASICs available for Cryptonight, which was designed to diminish the performance gap between CPUs, GPUs, and ASICs by demanding comparatively large amounts of memory (which are commonly available in today's PCs but very expensive to have in ASICs). This means that CPU mining is still possible, whereas in Bitcoin, CPU mining is utterly pointless. The hope is that this will encourage people to mine with existing computers, preventing too much centralization, like we see in Bitcoin with a few Chinese pools having the majority of Bitcoin hash rate.
As a consequence, CPU mining makes Monero more attractive to botnet miners as various (news) reports prove (e.g. 1, 2 and 3). This is an interesting point, because it harms zombies' owners, while benefiting Monero. While this can be seen as an overall plus, since botnets exist anyway, and are providing a good thing (Monero security) to society at large, instead of a bad one (sending spam, or serving child porn, or whatever it is they would do otherwise), it can also be interpreted as an additional (a presumably very strong) financial incentive to expand existing botnets and put more ressources into malware distribution.
On the other hand, the value of Bitcoin now has attracted a lot of miners, and it is vastly more costly to attack Bitcoin than to attack Monero. Hopefully this will change if Monero attracts a lot of attention from miners, but this is not a given.